Most masonary contractors would probably use a "pointing trowel" to do this kind of work. Pointing trowels come in widths from 5/16 inch to 1/2 inch (for concrete blocks) with the most common size for brickwork mortar joints being 3/8 inch.
Grout bags...(shown here), are typically used for applying the mortar or grout between irregular rocks (on fire places and such) or where the mortar joint is wider than 1/2 inch.
However, your masonary contractor will use whatever tool that he finds works best for him, and it's best to let him decide how to actually go about actually doing the work. As long as the mortar joints are repacked with new mortar, that's what matters. How that happens really doesn't matter as both a grout bag and a tuck pointing trowel are suitable for filling those joints with fresh mortar.